Prior to the present invention, somewhat analagous self-pressurized portable containers have been the subject matter of the U.S. Pat. No. 3,895,742 to Wulbern, and U.S. Pat. No. 3,989,170 and 3,929,262 and 3,880,323 to Viehe. FIG. 3 of the U.S. Pat. No. 3,895,742 most nearly is typical of existing prior art faucet connectors characterizing problems toward which the present invention is directed. One such problem was the fact of too much flexibility and collapse of the connector, buckling when an effort was made to force it onto a faucet outlet such as a spigot. Another problem arose from the failure of the faucet connector to hold onto the spigot when the water was turned-on, the pressure of the water in the faucet connector and in the hose and expanding self-pressurizable vessel's elastic membrane, resulting in the faucet connector merely losing its grip and thusly popping-off of the faucet, accidentally far too often. Also, these vessel combinations are commercially necessarily low-cost in order to be attractive and competitive in the commercial market place; thus, simple and inexpensive remedy was necessary in order to be acceptable and practical. Expensive or bulky faucet fasteners were thus ruled-out. Also, the connector had to be aesthetically attractive, rather than some unsightly structure. And most important, because the present combination is to be used by non-mechanically minded persons, the connector had to be simple to mount, and such that quick and easy mounting is possible. The achieving of so many requirements simultaneously posed considerable problems to be overcome.